Georges Reeb
modernPhilosophy of Mathematics / Non-Standard Analysis1920 – 1993
Georges Reeb (1920-1993) was a French mathematician known primarily for his contributions to differential topology and foliation theory, though he also engaged with philosophical questions about the foundations of mathematics. In his later years, he became a prominent advocate of non-standard analysis and raised philosophical questions about the nature of the mathematical continuum and the standard interpretation of natural numbers.
Notable Achievements
1
Proved the Reeb stability theorem in foliation theory
2
Pioneered philosophical defense of non-standard analysis
3
Developed the Reeb foliation, a key example in differential topology
4
Challenged standard assumptions about the naive integers and the mathematical continuum
5
Co-authored foundational work in the theory of foliations with Charles Ehresmann